Details

sample557.0ms

Algorithm

intervals

Results

357.0ms	3931×	body	80	nan
64.0ms	173×	body	640	valid
14.0ms	52×	body	320	valid
3.0ms	6×	body	1280	valid
2.0ms	21×	body	80	valid
1.0ms	4×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 6.6b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series279.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune366.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 0.7b

Counts

89 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
44×	`sqrt-prod`
40×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`times-frac`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `associate-/l*`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 107

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series353.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify73.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	634	1071
1	2335	978
2	5001	942

prune500.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Merged error: 0.3b

Counts

125 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
15.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series422.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify83.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	728	1296
1	2722	1176
2	5001	1134

prune584.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 0.2b

Counts

148 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.2b	(+ z (- 1.0 z))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
46×	`distribute-lft-out`
44×	`sqrt-prod`
42×	`times-frac`
35×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
12×	`associate-/r*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
4×	`pow1` `flip3-+` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--`

Counts

4 → 127

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
5.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series360.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(+ z (- 1.0 z))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify77.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	683	1179
1	2548	1073
2	5002	1031

prune560.0ms

Filtered

139 candidates to 82 candidates (59.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	142	6	148

Merged error: 0.1b

Counts

148 → 6

regimes647.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	50	23
2	50	23

end0.0ms

sample919.0ms

Algorithm

intervals

Results

596.0ms	6588×	body	80	nan
100.0ms	281×	body	640	valid
27.0ms	95×	body	320	valid
5.0ms	12×	body	1280	valid
3.0ms	30×	body	80	valid
2.0ms	11×	body	160	valid

Details

sample557.0ms

simplify29.0ms

prune5.0ms

localize23.0ms

rewrite36.0ms

series279.0ms

simplify47.0ms

prune366.0ms

localize26.0ms

rewrite43.0ms

series353.0ms

simplify73.0ms

prune500.0ms

localize27.0ms

rewrite45.0ms

series422.0ms

simplify83.0ms

prune584.0ms

localize35.0ms

rewrite41.0ms

series360.0ms

simplify77.0ms

prune560.0ms

regimes647.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample919.0ms

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